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3 4 5 7 = 24: 7 solutions

Difficulty: EasyOpen in Solver

3 × 4 + 5 + 7 = 24

  1. 3 × 4 = 12
  2. 5 + 7 = 12
  3. 12 + 12 = 24

7 solutions

  • 3 × 4 × (7 − 5) = 24Steps
    1. 3 × 4 = 12
    2. 7 − 5 = 2
    3. 12 × 2 = 24
  • 4 × 5 − (3 − 7) = 24Steps
    1. 4 × 5 = 20
    2. 3 − 7 = -4
    3. 20 − -4 = 24
  • 4 − 5 × (3 − 7) = 24Steps
    1. 3 − 7 = -4
    2. 5 × -4 = -20
    3. 4 − -20 = 24
  • 4 + 5 × (7 − 3) = 24Steps
    1. 7 − 3 = 4
    2. 5 × 4 = 20
    3. 4 + 20 = 24
  • (3 + 5) × (7 − 4) = 24Steps
    1. 3 + 5 = 8
    2. 7 − 4 = 3
    3. 8 × 3 = 24
  • 3 × (7 − (4 − 5)) = 24Steps
    1. 4 − 5 = -1
    2. 7 − -1 = 8
    3. 3 × 8 = 24

Solving hints

  • Build a factor pair: split the four numbers into two groups and try to make a factor pair of 24 — 3 × 8, 4 × 6, or 12 × 2 — then multiply the two groups.

  • No factor pair divides cleanly? Switch to sums: make two numbers add up to 24, or try shapes like (a ± b) × (c ± d) and (a + b + c) × d.

Related hands

FAQ

Can 3 4 5 7 make 24?

Yes. Every one of them is listed above with step-by-step working.

How many solutions does 3 4 5 7 have?

7 — the list above is exhaustive, so every mathematically distinct way to combine the numbers is shown.

How difficult is 3 4 5 7?

It is rated “Easy” on our four-tier scale, based on whether whole-number intermediate steps suffice, how many distinct solutions exist, and whether the hand includes a two-digit card (10–13).